M. Abtahi
Bull. Iran. Math. Soc. - , , - June, 2014 - (to appear) .
Publication year: 2014
‎Inspired by the work of Suzuki in‎
‎[T. Suzuki‎, ‎A generalized Banach contraction principle that characterizes metric completeness‎,
Proc‎. ‎Amer‎. ‎Math‎. ‎Soc. ‎136 (2008)‎, ‎1861–1869]‎,
‎we prove a fixed point theorem for contractive mappings‎
‎that generalizes a theorem of Geraghty in [M.A‎. ‎Geraghty‎, ‎On contractive mappings‎,
‎Proc‎. ‎Amer‎. ‎Math‎. ‎Soc., ‎40 (1973)‎, ‎604–608]
‎and characterizes metric completeness‎. ‎We introduce the family A of all nonnegative functions‎ ‎ϕ with the property that‎, ‎given a metric space (X,d) and a mapping T:XX‎, ‎the condition‎